Chapter 13.1, Problem 19PPS

To determine

To represent sample space for choice of quadrilaterals by Mr. G.

Answer to Problem 19PPS

(i) Organized List

{H,P},{H,R},{H,S},{H,T},{H,H}

{S,P},{S,R},{S,S},{S,T},{S,H}

(ii) Table

Outcomes	Square (S)	Rhombus( H )
Parallelogram	S,P	H,P
Rectangle	S,R	H,R
Square	S,S	H,S
Trapezoid	S,T	H,T
Rhombus	S,H	H,H

(iii) Tree Diagram

  

Explanation of Solution

Given information: An event where choice of quadrilaterals by Mr. G is represented

Explanation-

Let H represent the event that the quadrilateral is a rhombus.

Let S represent the event that the quadrilateral is a square.

Let R represent the event that the quadrilateral is a rectangle.

Let P represent the event that the quadrilateral is a parallelogram.

Let T represent the event that the quadrilateral is a trapezoid.

As one of the quadrilaterals must be having equal sides, so it has to be a square or rhombus.

On choosing between the quadrilaterals, the sample space will be represented as-

1. Sample Space using an organized list-
{H,P},{H,R},{H,S},{H,T},{H,H}

{S,P},{S,R},{S,S},{S,T},{S,H}

2. Sample Space using a table will be represented as-

Outcomes	Square (S)	Rhombus ( H )
Parallelogram	S,P	H,P
Rectangle	S,R	H,R
Square	S,S	H,S
Trapezoid	S,T	H,T
Rhombus	S,H	H,H

3. Sample Space using a tree diagram will be represented as-